30 Questions
What is the expansion of sin(x) in terms of x?
x - x^3/3! + x^5/5! -...
What is the limit of f(x) as x approaches a, if f(x) is an algebraic function?
It is a algebraic limit
What is the expansion of cos(x) in terms of x?
1 - x^2/2! + x^4/4! - x^6/6! +...
What is the expansion of tan(x) in terms of x?
x + x^3/3! + x^5/5! +...
What is the expansion of e^x in terms of x?
1 + x + x^2/2! + x^3/3! +...
What is the value of lim x → 0 (sin 2x / x)?
2
If f(x) = 2 sin(x) and g(x) = 3 cos(x), then what is the value of lim x → 0 (f(x) / g(x))?
2/3
What is the derivative of the function f(x) = tan(2x) using the chain rule?
2 sec^2(2x)
What is the value of lim x → 1 (G(x) - G(1)) / (x - 1) if G(x) = 25 - x^2?
1/24
What is the value of lim x → a (g(x) f(a) - g(a) f(x)) / (x - a) if f(a) = 2, f'(a) = 1, g(a) = 1, and g'(a) = 2?
3
What is the value of lim(x→∞) ((x+1)^2)/(x^2+2x)?
1
If a, b, c, and d are positive, then what is the value of lim(x→∞) ((a+bx)/(c+dx))?
e^(d/b)
What is the value of lim(x→∞) (1+x)^(1/x)?
e
What is the value of lim(x→0) (sin(x)/x)?
1
What is the value of lim(x→∞) (x^2+x-1)/(x^2+2x)?
1
What is the value of lim h → 0 (1 - cos(2h)) / sinh?
1/2
What is the value of lim x → 0 (x^2 sin(3x)) / sin(5x)?)
0
What is the value of lim x → 0 (tan(x) - sin(x)) / x^2?)
1/6
What is the value of lim x → 0 (sin(2x) / sin(5x))?)
2/5
What is the value of lim x → 1 (f(x) - f(1)) / (x - 1) if f(x) = 2 sin(x)?)
2
What is the value of lim x → 0 (sin(x) / x^2)?)
1/3
What is the value of lim x → 0 (cos(2x) - 1) / sin(x)?)
-2
What is the value of lim x → 0 (x^3 sin(3x)) / sin(5x)?)
0
What is the value of lim x → 0 (sin(3x) / sin(5x))?)
3/5
What is the value of lim x → 0 (tan(2x) - sin(2x)) / x^2?)
1/6
What is the Taylor series expansion of the function log(1 + x) around x = 0?
x - x^2/2 + x^3/3 -...
What is the condition for the function f(x) = (1 + 1/x)^x to be continuous at x = 0?
The function is not continuous at x = 0.
What is the derivative of the function f(x) = sin^(-1)x using the chain rule?
1 / sqrt(1 - x^2)
What is the limit of the function f(x) = (1 + x)^1/x as x approaches 0?
e
What is the Taylor series expansion of the function cosh(x) around x = 0?
1 + x^2/2 + x^4/4! +...
Test your understanding of various function expansions and identities used in calculus, including logarithmic, exponential, and trigonometric functions. Evaluate your knowledge of mathematical formulas and their applications. Improve your problem-solving skills in calculus with this quiz.
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